In this paper I concentrate on Euclidean diagrams, namely on those diagrams that are licensed by the rules of Euclid’s plane geometry. I shall overview some philosophical stances that have recently been proposed in philosophy of mathematics to account for the role of such diagrams in mathematics, and more particularly in Euclid’s Elements. Furthermore, I shall provide an original analysis of the epistemic role that Euclidean diagrams may (and, indeed) have in empirical sciences, more specifically in physics. I shall claim that, although the world we live in is not Euclidean, Euclidean diagrams permit to obtain knowledge of the world through a specific mechanism of inference I shall call inheritance.
According to Enactivism, cognition should be understood in terms of a dynamic interaction between an acting organism and its environment. Further, this view holds that organisms do not passively receive information from this environment, they rather selectively create this environment by engaging in interaction with the world. Radical Enactivism adds that basic cognition does so without entertaining representations and hence that representations are not an essential constituent of cognition. Some proponents think that getting rid of representations amounts to a revolutionary alternative to standard views about cognition. To emphasize the impact, they claim that this ‘radicalization’ should be applied to all enactivist friendly views, including, another current and potentially revolutionary approach to cognition: predictive processing. In this paper, we will show that this is not the case. After introducing the problem (section 2), we will argue (section 3) that ‘radicalizing’ predictive processing does not add any value to this approach. After this (section 4), we will analyze whether or not radical Enactivism can count as a revolution within cognitive science at all and conclude that it cannot. Finally, in section 5 we will claim that cognitive science is better off when embracing heterogeneity.
Ortega y Gasset is known for his philosophy of life and his effort to propose an alternative to both realism and idealism. The goal of this article is to focus on an unfamiliar aspect of his thought. The focus will be given to Ortega’s interpretation of the advancements in modern mathematics in general and Cantor’s theory of transfinite numbers in particular. The main argument is that Ortega acknowledged the historical importance of the Cantor’s Set Theory, analyzed it and articulated a response to it. In his writings he referred many times to the advancements in modern mathematics and argued that mathematics should be based on the intuition of counting. In response to Cantor’s mathematics Ortega presented what he defined as an ‘absolute positivism’. In this theory he did not mean to naturalize cognition or to follow the guidelines of the Comte’s positivism, on the contrary. His aim was to present an alternative to Cantor’s mathematics by claiming that mathematicians are allowed to deal only with objects that are immediately present and observable to intuition. Ortega argued that the infinite set cannot be present to the intuition and therefore there is no use to differentiate between cardinals of different infinite sets.
Reasoning from a naturalistic perspective, viewing the mind as an evolved biological organ with a particular structure and function, a number of influential philosophers and cognitive scientists claim that science is constrained by human nature. How exactly our genetic constitution constrains scientific representations of the world remains unclear. This is problematic for two reasons. Firstly, it often leads to the unwarranted conclusion that we are cognitively closed to certain aspects or properties of the world. Secondly, it stands in the way of a nuanced account of the relationship between our cognitive and perceptual wiring and scientific theory. In response, I propose a typology or classification of the different kinds of biological constraints and their sources on science. Using Boden’s (1990) notion of a conceptual space, I distinguish between constraints relating to the ease with which we can reach representations within our conceptual space (which I call ‘biases’) and constraints causing possible representations to fall outside of our conceptual space. This last kind of constraints does not entail that some aspects or properties of the world cannot be represented by us – as argued by advocates of ‘cognitive closure’ – merely that some ways of representing the world are inaccessible to us. It relates to what Clark (1986) and Rescher (1990) have framed as ‘the alien scientist hypothesis’ (the possibility that alien scientists, endowed with radically different cognitive abilities, could produce representations of the world that are unintelligible to us). The purpose of this typology is to provide some much needed clarity and structure to the debate about biological constraints on science.
Sigrid Mari Gjotterud, Erling Krogh, Cecilie Dyngeland and Nicholaus Solomon Mwakasumba
Transformative experiences can happen at unexpected times, in unexpected ways. This paper tells the story of how a gift of a goat can lead to the transformation of a life. Many organisations globally are engaged in a struggle to overcome poverty and injustice by providing livestock as a means for transformation. The animals in themselves are not enough for the transformed lives; they can be a valuable starting point. In the Uluguru Mountains in Tanzania, a Tanzanian and a Norwegian together took one such initiative in order to support teen-age orphans, one of the most vulnerable groups in the community who were struggling to survive. As practitioners and researchers, the four authors had been taking part in the development of the Mgeta Orphan Education Foundation (MOEF), which had developed through action learning/action research. Selected students received a goat and training, and the opportunity to join and develop a network of orphans throughout the region. In this article, we discuss the benefits and challenges the orphaned youngsters face when joining the foundation. How do they benefit from having the goat and what are the challenges, how do they learn and how do they contribute to fellow farmers in their communities? We claim that many of the students have experienced transformation, and provide examples to give evidence of this claim. However, the students are not the only ones who are transforming; so are we who, as co-researchers, have had the opportunity to play a role in and witness their efforts.
In this paper, we explain how our individual PhD enquiries (Farren, 2006; Crotty, 2012) have informed the philosophical underpinnings of our postgraduate programmes. The approach used to ensure validity and rigour in the research process is presented. We report on the development of the International Research Centre for e-Innovation and Workplace Learning and its collaboration in European projects such as Pathway to Inquiry Based Learning, Inspiring Science Education (ISE) and the African based Global e-Schools and Communities Initiative (GeSCI) project Leadership Development in ICT and the Knowledge Society. Our claim is that researching our own practice can be a transformative experience for the practitioner-researcher who is committed to generating knowledge that has personal, professional and social value.
In this article, I discuss the contribution of theoretical resources to the transformation in my thinking about professional development and accountability, within an action research self-study of practice as a civil servant, in the context of participation on the Doctor in Education (Leadership) programme at Dublin City University (DCU) in the period 2008-2012. It is at the intersection of these subject positions, between theory and practice, that professional development was explored through the ‘leadership problem’ of encouraging trainer colleagues to investigate the educational potential of information and communications technologies (ICT) for the development of their practice. Ultimately, this constituted a critical space for sustained dialogue between the self and the social in exploring professional subjectivity. The resources discussed supported the interrogation of social, cultural and historical conditions influencing self-understanding and narrative reasoning (Tamboukou, 2008) and movement from strategic to communicative reasoning (Habermas, 1984). It is claimed that this has significance for the development of a more educational training practice, which expresses a concern for subjectivity and agency in the face of a growing ‘performativity’ in professional life (Ball, 2003).
] Hartas, D. (2012). The Achievement Gap: Are Parents or Politicians Responsible. Bera Insights Autumn 2012.
 Herr, K. and Anderson, G. (2014). The Action Research Dissertation : A Guide for Students and Faculty, London: Sage.
 Hoel, N. (2013). Embodying the Field: A Researcher’s Reflections on Power Dynamics, Positionality and the Nature of Research Relationships. Fieldwork in Religion 8: 27-49.
 Jones, O. (2015). Don’t Let the Tories Steal Aspiration - We on the Left Must Claim It. The Guardian. London, UK